The high-frequency seismic field near the epicenter of a large earthquake is modeled by subdividing the fault plane into subelements and summing their contributions at the observation point. Each element is treated as a point source with an ω2 spectral shape, where ω is the angular frequency. Ground-motion contributions from the subsources are calculated using a stochastic model. Attenuation is based on simple geometric spreading in a whole space, coupled with regional anelastic attenuation (Q operator).
The form of the ωn spectrum with natural n follows from point shear-dislocation theory with an appropriately chosen slip time function. The seismic moment and corner frequency are the two parameters defining the point-source spectrum and must be linked to the subfault size to make the method complete. Two coefficients, Δσ and K, provide this link. Assigning a moment to a subfault of specified size introduces the stress parameter, Δσ. The relationship between corner frequency (dislocation growth rate) and fault size is established through the coefficient K, which is inherently nonunique. These two parameters control the number of subsources and the amplitudes of high-frequency radiation, respectively. Derivation of the model from shear-dislocation theory reveals the unavoidable uncertainty in assigning ωn spectrum to faults with finite size. This uncertainty can only be reduced through empirical validation.
The method is verified by simulating data recorded on rock sites near epicenters of the M8.0 1985 Michoacan (Mexico), the M8.0 1985 Valparaíso (Chile), and the M5.8 1988 Saguenay (Québec) earthquakes. Each of these events is among the largest for which strong-motion records are available, in their respective tectonic environments. The simulations for the first two earthquakes are compared to the more detailed modeling of Somerville et al. (1991), which employs an empirical source function and represents the effects of crustal structure using the theoretical impulse response. Both methods predict the observations accurately on average. The precision of the methods is also approximately equal; the predicted acceleration amplitudes in our model are generally within 15% of observations. An unexpected result of this study is that a single value of a parameter K provides a good fit to the data at high frequencies for all three earthquakes, despite their different tectonic environments. This suggests a simplicity in the modeling of source processes that was unanticipated.